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Reinventing the Wheel:

A Conceptual Approach for Teaching Arithmetic & Prealgebra. Barbara Lontz, Assistant Professor of Mathematics. Medea Rambish, Dean of Support Services . Overview. Discuss the national problem of under-preparedness .

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Reinventing the Wheel:

Presentation on theme: "Reinventing the Wheel:"— Presentation transcript:


Reinventing the Wheel:

A Conceptual Approach for Teaching Arithmetic & Prealgebra

Barbara Lontz, Assistant Professor of Mathematics

Medea Rambish, Dean of Support Services Slide2


Discuss the national problem of under-preparedness Learn about the course redesign :Concepts of Numbers

Participate in a sample lessonReview the evaluative outcome data, including achievement gap trendsShare the triumphs and struggles of bringing innovative ideas to scaleSlide3

National CrisisUnderpreparedness for college is a national problem

Developmental mathematics has been identified by Achieving the Dream as the biggest barrier to community college student successExperts say that new math teaching methodologies must be foundSlide4

MCCC Causes for ConcernThe success rates* for the past six years in our arithmetic classes have been declining

The success rates fell between 35% - 45%Our numbers reflect a national trend of declining math scoresTraditional arithmetic is taught through topics, (whole numbers, fractions, decimals, signed numbers)

*success rates are grades of C or betterSlide5

Concepts of NumbersAll learning outcomes of a traditional arithmetic course are covered but in a different order

Lessons proceed through concepts, (addition, subtraction, multiplication, division & combinations) using a discovery approachStudents are assessed on the same skills as the traditional arithmetic courseSlide6

Concepts' Guiding Principles

“Teach me, and I will forget. Show me, and I will remember. Involve me, and I will understand.” Chinese ProverbNew embedded skills are introduced on an as-needed basisIf a student understands a skill and its usefulness, practice problems can be kept to a minimum

Calculators are not needed in this courseAll students can learn math Slide7

Concepts of Numbers OutlineUnit 1: History of Numbers

Unit 2: The Real Number SystemUnit 3: ComparisonsUnit 4: AdditionUnit 5: SubtractionUnit 6: MultiplicationUnit 7: DivisionUnit 8: CombinationsSlide8

Unit 1: History of NumbersIn understanding the evolution of numbers, students will better understand/appreciate our present system

The following civilizations are covered: Babylonian Greek

Egyptian Roman African MayanThe concepts of place value and place holders are explored Slide9

Unit 2: The Real Number System

All sets of numbers are introduced: natural, whole, integers, rational, irrational & realNumbers are classified according to their sets Numbers are located on a number line

“All numbers are created equal.” B.LontzSlide10

Unit 3: ComparisonsThe

concepts of <, > and =“like” numbers are compared (integers, fractions with the same denominator)“unlike” numbers are compared (irrational numbers with rational numbers, fractions with different denominators, fractions with decimals)Numbers that are “like” are easier to compareSlide11

Unit 4: AdditionAddition (combining) of the following quantities:

whole numbers decimals

fractions integers algebraic expressionsApplication of the addition concept (perimeter, money problems)Identity element, commutative & associative properties, and binary operation concepts are introducedSlide12

Unit 5: SubtractionSubtraction (find differences) of the following quantities:

whole numbers decimals fractions

integers algebraic expressionsApplication of subtraction,(temperature, money problems)Solving equations that use the Addition PropertySlide13

Unit 6: MultiplicationMultiplications (repeated combinations) of the following quantities

whole numbers fractions decimals integers

algebraic expressions (distributive prop)ExponentsApplication of multiplication, (area, circumference, percents)Properties, e.g. commutative, associative, identity & inverseSlide14

Unit 7: DivisionDivision (repeated subtractions) of the following quantities:

whole numbers fractions decimals integers

Application of division, (percents, unit pricing)Solving equations using the Multiplication PropertySlide15

Unit 8: CombinationsSimplifying expressions involving multiple operations, (order of operations)

Solving multiple step applications, (ratio & proportion)Solving algebraic equations, 6(x+5) = -2(x -5)Slide16

Outcome Data

Success Rates: Success is a grade of C or better: Withdraws count as non-success

* the top 13% of Arithmetic Accuplacer scorers were accelerated into the next course (a 4 credit beginning algebra class)** an additional top 12% of Arithmetic Accuplacer scorers were accelerated into the next course (a 4 credit beginning algebra class)Slide17

Achievement Gap TrendsSlide18

Achievement Gap Trends

More recent data (fall 2011) show that a cohort of African American male students who receive mentoring do better in MAT 010 than African American male students who aren’t in the mentoring program.This data also show that the mentored

students’ success rates are higher than the overall success rate for MAT 010.Slide19

Discovery Approach

Locate the following points on the number line: 0.3,

, 2, , , , -1.5,  Slide20

What faculty say …

I can’t imagine ever going back to the traditional way of teaching this material. Chris Matus, West Chester UniversityMy students enjoy math more and therefore, I enjoy teaching more. Introducing them to some algebraic ideas early on has made

prealgebra easy to teach and more natural for the students. Steve Solomon, MCCC adjunctTo be honest, I didn’t think I would like it but my mind has been changed; the students enjoy it and I look forward to teaching it again. Joe Freiwald, MCCC retired FT facultySlide21

What students say ...“She explained the math to us in a way that I have never experienced. I thought it was taught to us to make sense..”

“You did not teach me math but you helped me learn math.” “With this course, I feel that I have learned so much and got to fully understand math and became good at it. I am a lot more confident about math now.”Slide22

Success Pipeline – Math RedesignSlide23

Scaling a Promising Practice

Institution buy-in Ω financial

Ω time for developmentDepartment approval Ω bringing to a larger scale Ω faculty willingness to try something new Ω trainingMonitoring/AssessmentFall 2011 Concepts received a William And Flora Hewlett Scaling Innovation Project two-year grant through the Community College Research Center (CCRC) to replicate at other colleges and improve learning within Slide24


Barbara Lontz blontz@mc3.edu

Medea Rambish mrambish@mc3.edu Slide25

Planning and plodding wins the race”

The Tortoise and the Hare, Aesop